Atkin-Lehner |
2- 3- 5+ 7+ 11+ |
Signs for the Atkin-Lehner involutions |
Class |
69300z |
Isogeny class |
Conductor |
69300 |
Conductor |
∏ cp |
96 |
Product of Tamagawa factors cp |
deg |
663552 |
Modular degree for the optimal curve |
Δ |
-248134453008750000 = -1 · 24 · 314 · 57 · 73 · 112 |
Discriminant |
Eigenvalues |
2- 3- 5+ 7+ 11+ 2 -2 4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,61800,-23225375] |
[a1,a2,a3,a4,a6] |
Generators |
[380:7425:1] |
Generators of the group modulo torsion |
j |
143225913344/1361505915 |
j-invariant |
L |
5.9815938025617 |
L(r)(E,1)/r! |
Ω |
0.15411279781871 |
Real period |
R |
1.6172120592104 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999998264 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
23100x1 13860m1 |
Quadratic twists by: -3 5 |